negace

Negace is the term used in Czech and related languages to denote negation, the operation of denying or contradicting a statement, proposition, property, or statement. In a formal context, negace is the act of making something false or opposite. The concept is central to logic, linguistics, and computer science.

In logic and mathematics, negace (logical negation) is a unary operator that takes a proposition p to its negation ¬p, which has the opposite truth value of p. The basic rule is that if p is true, ¬p is false, and if p is false, ¬p is true. In propositional logic, double negation yields p (¬(¬p) ≡ p); De Morgan's laws relate negation to conjunction and disjunction (¬(p ∧ q) ≡ ¬p ∨ ¬q; ¬(p ∨ q) ≡ ¬p ∧ ¬q).

In linguistics, negace refers to the grammatical or syntactic process of forming negative statements. This often involves negative particles or affixes that modify verbs, adjectives, or entire clauses. For example, in many Slavic languages, a negative marker such as ne- attaches to the verb to negate a sentence; in English, the negation is expressed with 'not' as part of the auxiliary 'do' construction or a copula with negation: "The cat is not on the mat." The scope of negation and its interaction with quantifiers or polarity items are topics of study in semantics.

In everyday use, negace helps express denial, contradiction, or absence of a property. The concept is widely applied across disciplines, from formal proofs to natural language processing.